The multi-terminal maximum-flow network-interdiction problem

Abstract

a b s t r a c tThis paper defines and studies the multi-terminal maximum-flow network-interdiction problem (MTNIP) in which a network user attempts to maximize flow in a network among K P 3 pre-specified node groups while an interdictor uses limited resources to interdict network arcs to minimize this maximum flow. The paper proposes an exact (MTNIP-E) and an approximating model (MPNIM) to solve this NP-hard problem and presents computational results to compare the models. MTNIP-E is obtained by first formulating MTNIP as bi-level min-max program and then converting it into a mixed integer program where the flow is explicitly minimized. MPNIM is binary-integer program that does not minimize the flow directly. It partitions the node set into disjoint subsets such that each node group is in a different subset and minimizes the sum of the arc capacities crossing between different subsets. Computational results show that MPNIM can solve all instances in a few seconds while MTNIP-E cannot solve about one third of the problems in 24 hour. The optimal objective function values of both models are equal to each other for some problems while they differ from each other as much as 46.2% in the worst case. However, when the postinterdiction flow capacity incurred by the solution of MPNIM is computed and compared to the objective value of MTNIP-E, the largest difference is only 7.90% implying that MPNIM may be a very good approximation to MTNIP-E.

Effects of a Player's Awareness of Information Acquisition and Ability to Change Strategy in Attrition Games

“…We simply use R (2) 0 and B (2) 0 unless they confuse our theory, for the sake of simplicity. For the one-shot game in Stage 2, Γ(R (2) 0 , N l , B (2) 0 ), Hohzaki and Chiba show that the attrition of the attackers is given by the product of B (2) 0 (y (1) ) and the optimal value ν * l of the following linear programming problem.…”

“…e remaining members of Stage 2 by y (2) = {y (2) e , e ∈ A}. We use E An overview of the solution by Hohzaki and Chiba [25] is as follows.…”

“…After knowing the results of Stage 1 (the attacker's present node i, the number of surviving attackers R (2) 0 , and the number of remaining defenders B (2) 0 ), both players can anticipate their optimal strategies in Stage 2 by solving the one-shot game Γ(R (2) 0 , i, B (2) 0 ). As seen as a general property of the equilibrium point, neither player can benefit from deviating from their equilibrium strategy.…”

“…Fulkerson and Harding [19], Golden [22], Bayrak and Bailey [9], and Cappanera and Scaparra [13] analyzed an optimal resource allocation problem in shortest-path networks in which the distributed resource changes some attributes of the network, such as arc lengths. Wood [51] discussed a Stackelberg game on the maximum flow on a network, and Akgün et al [2] dealt with a Stackelberg game of an interdiction problem with multicommodity maximum flows referred to as the multi-terminal maximum-flow network-interdiction problem.…”

A Study on Material Transportation Capability Analysis Method in NK using Scenario-based Simulation

“…[12] . 상기 네트워크의 특징은 다중 터미널(multi-terminal) [10] 이고, 보급거리가 신장됨으로써 중간보급기지인 전방지원대가 운용되고 있다. 이상의 행군대열로 구성된다 [12] .…”